From the experimental data, J-integral for a DCB specimen was calculated by using the following relationship ( Anthony Paris, 1988 ): (6.6) J 2 P b where P is the reaction force at the loading pin location measured during the DCB experiment, is rotation at the loading pin acquired through DIC calculation, and b is the width of the specimen.For an isotropic material, it is represented by three parameters: the critical energy release rate, the critical tensile cohesive failure stress and the shape of the tractionseparation law.
The numerical value of the initial damage parameter, d init, is usually close to unity. The damage parameter, d, quantifies the evolution of damage and is defined as follows: (11.17) d min ( d p, 1 n nc ) where d p is the value of the damage parameter in the previous load step and the operator is defined as x x if x 0 otherwise. As the decrease in d monotonically takes place, according to Eqn (11.17), damage is not recovered upon unloading and the cohesive zone is not healed as shown in Figure 11.12. If reloading occurs, the stiffness of the cohesive zone keeps its most recent value and decreases according to the cohesive separation law up to failure. ![]() Dadfarnia,. P. Schembri, in Gaseous Hydrogen Embrittlement of Materials in Energy Technologies: Mechanisms, Modelling and Future Developments, 2012 Parameter sensitivity of simulation results To investigate the effect of the stiffness of the traction- separation law upon grain boundary opening on crack propagation, we carried out simulations by varying the parameter Q 1 when the cohesive stress is ( m ) 0 4 0. ![]() This is in agreement with the work of Tvergaard and Hutchinson 17 in which they found that the shape of the traction separation law, as long as the maximum stress and the work of separation remain the same, has relatively weak effect on the crack propagation velocity. Effect of the parameter Q 1 (see Fig. In both experiments and simulations, the specimen was bolt-loaded at K I 0 57.8 MPa m in hydrogen gas at pressure 207 MPa (external embrittlement). In the simulations, D int D and m 10. Figure 11.11 shows the effect of the grain boundary diffusion coefficient D int on crack propagation while the bulk hydrogen diffusion coefficient D is kept constant as reported in Table 11.1. Clearly, faster diffusion along the grain boundaries accelerates crack growth at the early stages and improves agreement with the experimental velocities. In addition, we find in the simulations that crack is always arrested after 17 mm of growth regardless of the magnitude of the grain boundary diffusion coefficient D int. The reason is that the faster grain boundary diffusion coefficient governs the time of arrest but not the propagation distance which is governed by the complex interaction between hydrogen transport and material deformation as the crack advances. We emphasize here that our approach to simulating crack arrest does account for the fact that a decreasing applied stress intensity factor enables crack arrest. In fact, our simulations of crack arrest do reflect the interaction of a continuously decreasing applied stress intensity with a decreasing grain boundary cohesion according to our proposed thermodynamic model of decohesion. Sensitivity of crack growth to the grain boundary diffusion coefficient D int when the cohesive stress is ( m ) 0 20 GPa. The bulk hydrogen diffusion coefficient is D 1.66 10 15 m 2 s. Traction Separation Law Full Chapter URLView chapter Purchase book Read full chapter URL: Damage simulations in composite structures in the presence of stress gradients J. Reinoso,. F. Pars, in Modeling Damage, Fatigue and Failure of Composite Materials, 2016 Local analysis of configurations 1 and 2 The interlaminar damage estimations obtained for panel 1 using CZM following a bilinear TSL are depicted in Figure 18.11 for the two globallocal procedures (submodeling, Figure 18.11(a), and coupling, Figure 18.11(b) ) at load levels 80, 100 (first ultrasound inspection), and 150 kN (second ultrasound inspection). This latter value corresponded to the load level limit at which the prescribed conditions on the submodeling approach were still representative. Both techniques predicted that the failure process was initiated at around 50 kN. As was discussed in Refs 6,7, both methodologies estimated that the damage growth path ran mostly longitudinally around the joint as a consequence of the existing high stress concentration at the stringer web termination. These predictions accurately agreed with the ultrasound measurements, from which similar debonding patterns were obtained ( Figure 18.6 ). It can be observed therefore that both techniques, submodeling and coupling, lead to similar results; submodeling is used in what follows. ![]() Submodeling. (b) Coupling shell-to-solid technique. View chapter Purchase book Read full chapter URL: Multi-scale modeling of high-temperature polymer matrix composites for aerospace applications S. Roy, in Structural Integrity and Durability of Advanced Composites, 2015 6.4 Extraction of cohesive law from experimental data through J-integral For a monotonically increasing deformation within the process zone, the cohesive traction separation law relates the stress state across the failure zone to the local separation distance. It is assumed that the cohesive stress depends on the local separation and its rate, and that a critical opening separation exists, beyond which the cohesive stress vanishes. The cohesive law approach is particularly attractive for modeling large-scale bridging (LSB) process zones ( Sorensen Jacobsen, 2003 ) where process zone size in one direction is very large compared with other directions. To determine the cohesive stresses, the J-integral as a function of crack opening displacement (COD) was determined experimentally.
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